SERIATIOK AND PLOTTING OF DATA. 17 



When C is small, say less than 10%, the factor in brackets 

 may be omitted, especially as only two significant figures 

 of the probable error need be recorded* 



The average, standard deviation, coefficient of correlation, 

 and their probable errors may be conveniently calculated al- 

 together by logarithms, as shown in the paradigm on page 38. 



QUICK METHODS OF ROUGHLY DETERMINING AVERAGE AND 

 VARIABILITY.* 



1. Arrange the specimens in a series according to the mag- 

 nitude of the character, simply judging the order by the eye. 

 Then pick out those two that will divide the series into thirds 

 and measure them. Their average will be the average of the 

 whole series. Then, 



Mean the smaller of the two measures 



- 



(.43 is the value of - , at which the area of the curve 

 o 



included between these limits of x equals one-third of the 

 whole) . 



Or, 2. Select roughly two specimens that seem to be about 

 one-third of the distance from the two extremes nd group 

 all others as larger than the larger one, smaller than the 

 smaller one, or between the two. Measure the two speci- 

 mens. Count the number in each group and determine a 

 by aid of Table IV (p. 120) as follows: Taking as origin the 

 middle of the whole series, call the number of leaves from 

 the middle to the smaller n/, and the number from the 

 middle to the larger n 2 ". Also, the x distance to the lower 

 division point /^ and to the upper division point h 2 . Then 

 (/ij-|-/& 2 ) = the range covered by the middle division or the 

 difference between the upper and lower value. As we know 

 the areas of the curve between the origin and /^ on the one 

 hand and h 2 on the other (percentage of individuals between 



the middle and h t and h 2 ), we can find and from Table IV, 



o o 



since they are the values corresponding to the percentage 

 * See Macdonell, 1902. 



